Tutte seminar - Alexander Barvinok

The number of matrices and a random matrix with prescribed row and column sums and 0-1 entries

Abstract:

Let us consider the set of 0-1 matrices with prescribed row and column sums as a finite probability space with the uniform measure. I will present an asymptotic formula for the number of such matrices and also describe what a random matrix is likely to look like. We'll also discuss what a random graph with the prescribed degree sequence looks like and how many such graphs are there. 

This talk is partially based on a joint work with J.A. Hartigan (Yale).